PhD Courses

Courses 2025-26
SSD	Name of the course	Professor	Semester	Language	Credits
MAT/05 (BA)	Elliptic-parabolic degenerate operators	Biagi, Bramanti	Spring	English	5
SECS-S/01 (BA)	Advanced Statistical Learning for complex data	Ieva		English	5
MAT/07 (BA) MAT/06	Introduction to Entropy	Jaksic	Winter	English	5
MAT/08 (BA) MAT/03	Analytic and topological aspects in Scientific Machine Learning	Lella, Regazzoni	Winter	English	5
MAT/08 (SC)	Numerical Algorithms for Optimization	Formaggia, Verani	Winter	English	5
MAT/05 (SC)	Some mathematical aspects of Nonlinear Diffusion	Muratori, Volzone	Winter	English	5
	Advanced mathematical methods in engineering I	Correggi			5
	Advanced mathematical methods in engineering II	Correggi			5

Today's events

may 18 mon 2026

Seminar
Eugene Y.S. Chua, New Balances: Finding Equilibria in Quantum Statistical Mechanics, 05-18-2026, 14:30
- Seminar
- Eugene Y.S. Chua
- Nanyang Technological University, Singapore
- New Balances: Finding Equilibria in Quantum Statistical Mechanics
- Monday, 18 May 2026 at 14:30
- Sala Consiglio VII Piano, Edificio 14 Nave, Dipartimento di Matematica
- Abstract
  
  There is a tension in the foundations of thermodynamics. Philosophers argue that certain non-classical systems — black holes, relativistic systems, self-gravitating systems — do not ‘really’ behave thermodynamically. Nonetheless, physicists continue to extend thermodynamic — or thermodynamic-like — concepts into these and other exotic regimes. We situate and analyze this tension for the concepts of thermal equilibrium and equilibration in quantum statistical mechanics. First, we show how these concepts break down in three classes of quantum systems heavily discussed in quantum statistical mechanics: integrable systems, many-body localized systems, and periodically driven systems. Second, physicists nevertheless aim at — and succeed in — recovering other equilibrium-like concepts in and around these regimes, each with their own limited domains of applicability. While these concepts are not the classical ones, we argue that these concepts instantiate a broader mode of generalized equilibrium reasoning — a search for generalized equilibria with the following features: the scale-relative search for stationarity, stability under perturbation, and equilibration. We end by ruminating on whether it matters if such states are “really” thermodynamic, and on the role of generalized equilibrium reasoning in physics.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

Upcoming events

may 19 tue 2026

Seminar
Edoardo Mainini, Gradient flows: from diffusion to Keller-Segel models, 05-19-2026, 15:15
- Seminar
- Edoardo Mainini
- Università di Genova
- Gradient flows: from diffusion to Keller-Segel models
- Tuesday, 19 May 2026 at 15:15
- Aula seminari, terzo piano
- Abstract
  
  We discuss the gradient flow approach to aggregation-diffusion models of Keller-Segel type. We prove regularizing effect and sharp hypercontractivity estimates. As a consequence, we deduce several properties such as existence of solutions with measure data, energy dissipation identity, evolution variational inequalities and uniqueness, thus establishing a full parallel with the theory of gradient flows for diffusion models and geodesically convex functionals.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 20 wed 2026

Seminar
Paula Cerejeiras, Non-classical Howe duality for \(\mathbb Z_3\)-graded Clifford algebras, 05-20-2026, 00:00 precise
- Seminar
- Paula Cerejeiras
- Universidade de Aveiro
- Non-classical Howe duality for \(\mathbb Z_3\)-graded Clifford algebras
- Wednesday, 20 May 2026 at 00:00 right
- In presenza (aula seminari Mox sesto piano) e on-line (il link zoom verrà reso disponibile il giorno stesso del seminario)
- Abstract
  
  \(\mathbb Z_3\)-graded Clifford algebras were developed having in mind concrete applications in physics, such as quarks and hypersymmetry, or the N-body problem. In this talk we discuss the main ingredients for the study of Dirac operators in this setting: the Howe duality, the Fischer decomposition and the Cauchy-Kovalevskaya extension. By passing, we also will discuss -time permits - possible applications.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 21 thu 2026

MOX Seminar
Caterina Gregorio, Statistical methods for health trajectories in aging and chronic Illness, 05-21-2026, 15:45
- MOX Seminar
- Caterina Gregorio
- Karolinska Institutet
- Statistical methods for health trajectories in aging and chronic Illness
- Thursday, 21 May 2026 at 15:45
- Aula Saleri - Sesto piano Dipartimento di Matematica
- Abstract
  
  Aging is a complex, lifelong process characterized by the accumulation of chronic conditions, functional decline, and increasing heterogeneity in health trajectories. Improving our understanding of aging is essential for identifying critical windows for prevention and intervention in older populations. However, longitudinal aging studies pose substantial statistical challenges due to intermittent observation, partial observability of health trajectories, and the presence of multiple biological processes evolving continuously over time.
  In this seminar, I will present my current research on the development and application of statistical methodologies to address etiological questions in aging research and to construct longitudinal aging metrics that support inference, individualized prediction, and data-driven evaluation of preventive interventions for healthy aging.
  The focus will be on extensions of classical multistate models that address interval censoring and hidden states, as well as on multivariate mixed latent formulations motivated by research questions in dementia, multimorbidity, and biological aging. Simulation studies and applications to population-based aging cohorts are used to evaluate model performance and to illustrate the practical implementation of these methods.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 25 mon 2026

Seminar
Gabriele Sbaiz, Environmental impact into multi-objective portfolio allocations, 05-25-2026, 13:15
- Seminar
- Gabriele Sbaiz
- University of Trieste
- Environmental impact into multi-objective portfolio allocations
- Monday, 25 May 2026 at 13:15
- Aula seminari, 3° piano, e online (Microsoft Teams) shorturl.at/hLHGu
- Abstract
  
  In this talk, we tackle a sustainable multi-objective optimization problem in which we aim to maximize a mean-risk ratio while, at the same time, minimizing the environmental impact.
  More specifically, the mean-risk metric is represented by the Stable Tail Adjusted Return ratio, which penalizes only downside tail-risk and incorporates skewness and fat-tail information. In the portfolio construction, we consider the classical constraints concerning full investment and buy-in threshold requirements.
  To deal with these new asset allocation models, we develop an improved Multi-Objective Particle Swarm Optimizer (MOPSO) embedded with a repair-projection mechanism to satisfy the constraints. Moreover, we implement a deep learning architecture to improve the estimation quality of the mean-risk measure and to speed up the MOPSO solver.
  Finally, we conduct empirical tests on a European dataset to illustrate the effectiveness of the proposed strategies, accounting for different levels of environmental awareness.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 26 tue 2026

Seminar
Serena Federico, Weyl calculus on graded Lie groups, 05-26-2026, 11:00
- Seminar
- Serena Federico
- Dipartimento di Matematica, Università di Bologna
- Weyl calculus on graded Lie groups
- Tuesday, 26 May 2026 at 11:00
- Sala Consiglio VII Piano, Edificio 14 Nave, Dipartimento di Matematica
- Abstract
  
  In this talk, we shall discuss the existence of a Weyl pseudo-differential calculus on a graded Lie G. To begin with, we will introduce a family of admissible quantizations on G and develop the corresponding pseudo-differential calculus. Afterwards, following classical criteria, we shall identify the suitable candidate Weyl quantization on G among all the admissible symmetric ones. Finally, we will show that in the case of the Heisenberg group, the Weyl quantization is uniquely determined.
  
  This talk is based on a joint work with D. Rottensteiner and M. Ruzhansky.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 04 thu 2026

MOX Seminar
Matteo Fontana, Distribution-Free Inference for Multivariate Outputs and Time-Dependent Observations, 06-04-2026, 12:30
- MOX Seminar
- Matteo Fontana
- Royal Holloway University of London
- Distribution-Free Inference for Multivariate Outputs and Time-Dependent Observations
- Thursday, 4 June 2026 at 12:30
- aula Saleri - Sesto piano Dipartimento di Matematica
- Abstract
  
  Conformal prediction delivers finite-sample, distribution-free coverage guarantees, but its classical formulation is largely confined to univariate outputs and exchangeable observations. In this seminar I present two contributions that extend the framework along these axes.
  The first concerns multi-output conformal regression. I introduce a unified comparative study of nine methods - marginal, density-based, and sample-based - that clarifies their theoretical relationships and reveals that several sample-based methods are special cases of density-based ones. Within this framework I propose two novel classes of conformity scores: CDF-based scores, yielding a method (C-PCP) that achieves asymptotic conditional coverage using only samples from a generative model; and latent-based scores, yielding a computationally efficient method (L-CP) for invertible generative models. A large-scale empirical study across thirteen datasets confirms the predicted ordering of methods on conditional coverage, region size, and computational cost.
  The second contribution addresses multi-step forecasting under temporal dependence. I introduce JANET, which extends generalised conformal prediction from the transductive to the inductive setting and constructs joint prediction regions controlling the K-familywise error rate - a more flexible criterion than FWER for long horizons. The framework provides exact validity for independent series and approximate validity for single series under weak ergodicity, matching bootstrap alternatives at a fraction of the cost.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 08 mon 2026

jun 12 fri 2026

WorkShop
Bifurcations in differential equations
06/08/2026 - 06/12/2026
- WORKSHOP
- BIFDE26
  Bifurcations in differential equations
- organizers
  Maurizio Garrione, Filippo Gazzola (Politecnico di Milano), Giulio Ciraolo (University of Milan)
- Monday, 8 June 2026 - Friday, 12 June 2026
  Aula Consiglio - 7th floor, Building 14, Politecnico di Milano, Via Bonardi 9, 20133 Milano (Italy)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 11 thu 2026

MOX Seminar
Lilit Yeghiazarian, The Power Of Connected Data: How Knowledge Networks Help Address Urban Flooding And Water-Energy Challenges, 06-11-2026, 14:30
- MOX Seminar
- Lilit Yeghiazarian
- University of Cincinnati
- The Power Of Connected Data: How Knowledge Networks Help Address Urban Flooding And Water-Energy Challenges
- Thursday, 11 June 2026 at 14:30
- Aula seminari, III piano, Dipartimento di Matematica, Politecnico di Milano
- Abstract
  
  Cities are highly interconnected networks of networks (referred to as the Urban Multiplex) that include the power grid and transportation networks, surface water and groundwater, sewerage and drinking water systems, inland navigation and dams – all intertwined with the natural environment and socioeconomic and public health sectors. While the Urban Multiplex is physically and functionally connected, the data produced within its individual sectors are not. This prevents us from fully understanding how the Urban Multiplex is connected, and how failures triggered by external stressors like floods cascade.
  
  Knowledge Networks are an AI technology that (i) integrates Urban Multiplex data, (ii) produces real-time flood forecasts across the continental U.S., (iii) evaluates the total impact of floods on cities, and (iv) supports queries at the nexus of water and energy, and beyond. This talk will describe the development of the Urban Flooding and Water-Energy Nexus Open Knowledge Networks that aim to provide actionable answers to questions such as:
  
  1. Real-time flood mitigation and response: Will my neighborhood flood? Will I have access to water and power? Will this storm disrupt the power grid, drinking water treatment plant, or a bridge?
  
  2. Long-term design, planning and research: What is the total socioeconomic impact of this flood? Which critical urban infrastructure will likely fail in a future flood? Which failures will affect the most people or the most vulnerable people? Are there vulnerable communities downstream of this coal mine?
  
  The interdisciplinary team behind this project has brought together academic researchers, industry, federal government, U.S. National labs and local stakeholders. It is funded by the U.S. National Science Foundation’s Proto-OKN (Open Knowledge Network) and Convergence Accelerator Programs that are
  developing critical national data infrastructure as an open knowledge network. It enables rapid advancement in highly complex problems of critical societal importance.
  
  This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
  
  Contatto:
  luca.formaggia@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 15 mon 2026

jun 19 fri 2026

WorkShop
Indam workshop: geometry of severi varieties and hurwitz spaces
06/15/2026 - 06/19/2026
- WORKSHOP
- Indam workshop: geometry of severi varieties and hurwitz spaces
- organizers
  K. Christ, S. Molcho, S. Torelli
- Hurwitz spaces and Severi varieties are among the most classical spaces studied in algebraic geometry, going back to the beginnings of modern algebraic geometry in the second half of the 19th century. Since that time, they have remained central objects in the theory of algebraic curves. Though very classical objects, new techniques have in recent years been used to find answers to old questions, and to establish many new connections. The aim of the workshop is to bring together experts in these various approaches in order to explore further applications and possible synergies. Particular areas of focus are the global geometry of Severi varieties and Hurwitz spaces, as well as relations to Brill Noether theory and to the moduli space of curves and its subloci.
- Monday, 15 June 2026 - Friday, 19 June 2026
  Palazzone di Cortona, Cortona, Italy.
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 23 tue 2026

MOX Seminar
Giovanni Stabile, Model Reduction and Scientific Machine Learning for Environmental and Urban Flows, 06-23-2026, 14:00
- MOX Seminar
- Giovanni Stabile
- Scuola Sant'Anna di Pisa
- Model Reduction and Scientific Machine Learning for Environmental and Urban Flows
- Tuesday, 23 June 2026 at 14:00
- Aula Saleri
- Abstract
  
  The global population is increasingly concentrated in urban areas, with projections indicating that up to 80% will reside in cities by 2050. This trend underscores the need for efficient and reliable tools to model the urban microclimate, which play a key role in supporting urban planners and policymakers in designing more sustainable and livable environments.
  
  At the urban scale, pollutant dispersion is strongly influenced by transient atmospheric conditions, requiring high-fidelity computational fluid dynamics (CFD) simulations with fine spatial resolution and small time steps. These requirements lead to substantial computational and memory demands, often necessitating access to high-performance computing (HPC) resources to obtain results within practical time frames.
  
  To address these challenges, surrogate modeling techniques offer a promising alternative, enabling rapid predictions with controlled accuracy loss. In this talk, I will present recent advances in numerical methods for real-time and many-query simulations of urban microclimate dynamics. The discussion will cover projection-based reduced-order models, physics-informed neural networks, graph neural networks, and scale-adaptive simulation strategies. This research is developed within the framework of the ERC Starting Grant DANTE.
  
  Contatto:
  nicola.parolini@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 25 thu 2026

MOX Colloquia
Lars Ruthotto, Scientific Machine Learning in High Dimensions , 06-25-2026, 14:30
- MOX Colloquia
- Lars Ruthotto
- Departments of Mathematics and Computer Science, Emory University
- Scientific Machine Learning in High Dimensions
- Thursday, 25 June 2026 at 14:30
- Sala Consiglio VII piano - Dipartimento di Matematica
- Abstract
  
  Many problems at the frontier of scientific machine learning reduce to solving high-dimensional partial differential equations: Hamilton–Jacobi– Bellman equations in optimal control, the continuity equation and Fokker–Planck equation in generative modeling, and coupled systems in mean-field games and Bayesian inverse problems, to give some examples. While the reach of classical numerical methods is limited by the curse of dimensionality, recent advances at the interface of numerical analysis and machine learning are beginning to change that picture by combining classical mathematical structure with neural-network approximation and Monte-Carlo-style sampling.
  
  In this talk I will discuss the mathematical and computational foundations of these methods with a focus on high-dimensional stochastic optimal control. I will draw on selected results from our group's work on neural HJB solvers, conditional optimal transport for Bayesian inference, and mean-field-games, and place them in the broader landscape of methods that have emerged in recent years.
  
  I will outline the main challenge of closing the gap between theoretical guarantees and
  practical performance. I will emphasize the role of sampling in determining whether neural methods discover the structure of high-dimensional value functions, the design of benchmarks, and the choice of discretization and adjoint formulations when differentiating through neural SDEs. I will close with open questions and opportunities for the scientific machine learning community.
  
  This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
  
  Contatto:
  paolo.zunino@polimi.it
- Lars Ruthotto
  Lars Ruthotto is the Winship Distinguished Research Associate Professor in the Departments of Mathematics and Computer Science at Emory University, where he is a member of Emory's Scientific Computing Group and directs the Emory REU/RET Site for Computational Mathematics for Data Science. He earned his Diploma (2010) and PhD (2012) in Mathematics from the University of Münster, Germany, and was a postdoc at the University of British Columbia before joining Emory. His research develops computational methods at the interface of scientific computing, optimization, machine learning, and inverse problems, with recent emphasis on neural-network methods for high-dimensional partial differential equations and stochastic optimal control. He is a recipient of the NSF CAREER Award, serves as a Section Editor for the SIAM Journal on Scientific Computing, and is supported by the US NSF and the Office of Naval Research.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 29 mon 2026

jul 03 fri 2026

WorkShop
Commutative algebra and algebraic geometry in milan
06/29/2026 - 07/03/2026
- WORKSHOP
- CAAG26
  Commutative algebra and algebraic geometry in milan
- organizers
  A. Constantinescu, A. D'Alì, P. Lella, A. Sammartano
- The conference will be focused on the interplay between topics in commutative algebra, such as syzygies and singularities, and topics in algebraic geometry, such as moduli spaces and rationality problems. Speakers Ayah Almousa (University of Kentucky) Benjamin Briggs (Imperial College London) David Eisenbud (UC Berkeley) Eleonore Faber (University of Graz) Gavril Farkas (Humboldt-Universität zu Berlin) Michele Graffeo (SISSA Trieste) Eloísa Grifo (University of Nebraska-Lincoln) Srikanth Iyengar (University of Utah) Joachim Jelisiejew (University of Warsaw) Patricia Klein (Texas A&M University) Margherita Lelli-Chiesa (Università degli Studi Roma Tre) Alex Massarenti (Università degli Studi di Ferrara) Irena Peeva (Cornell University) Claudia Polini (University of Notre Dame) Elisa Postinghel (Università degli Studi di Trento) Claudiu Raicu (University of Notre Dame) Ritvik Ramkumar (University of Notre Dame) Francesco Russo (Università degli Studi di Catania) Alexandra Seceleanu (University of Nebraska-Lincoln) Bernd Ulrich (Purdue University) Keller VandeBogert (University of Kentucky) Matteo Varbaro (Università degli Studi di Genova
- Monday, 29 June 2026 - Friday, 3 July 2026
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 02 thu 2026

MOX Seminar
Matteo Pegoraro, Topological Data Analysis: Invariance Properties, Statistical Problems, and Topological Machine Learning, 07-02-2026, 14:30
- MOX Seminar
- Matteo Pegoraro
- Università Svizzera Italiana
- Topological Data Analysis: Invariance Properties, Statistical Problems, and Topological Machine Learning
- Thursday, 2 July 2026 at 14:30
- Aula saleri - Sesto piano Dipartimento di Matematica
- Abstract
  
  I will present some of my contributions to Topological Data Analysis through the problem of building rigorous and usable TDA pipelines. Starting from a function, mesh, or point cloud, one builds a filtration and extracts a topological summary, such as a persistence diagram, merge tree, or Reeb graph. I will discuss how these summaries encode coordinate-free and invariant information, and why turning this idea into a robust mathematical pipeline requires carefully designed metrics, stability results, and estimation procedures, using tools from topology, geometry, statistics, and optimal transport.
  
  This perspective also exposes a second difficulty: even once stable summaries have been constructed, many of them naturally live in non-linear metric spaces, making standard statistical and machine-learning methods difficult to apply directly. I will therefore conclude with recent work on Persistence Spheres, an explicit Hilbert-space embedding of persistence diagrams with provable bi-continuity, aimed at making topological summaries compatible with modern machine-learning pipelines.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
aug 31 mon 2026

sep 03 thu 2026

WorkShop
Late summer conference in geometric analysis
08/31/2026 - 09/03/2026
- WORKSHOP
- Late summer conference in geometric analysis
- organizers
  Luca Benatti, Mattia Fogagnolo, Alessandra Pluda, Marco Pozzetta, Alberto Roncoroni.
- This event brings together an international group of specialists to discuss cutting-edge topics in Geometric Analysis, such as minimal surfaces, isoperimetric problems, Lorentzian geometry, general relativity, geometric evolution equations, and geometric problems in the calculus of variations. Our goal is to turn recent progress into meaningful exchanges, giving participants fresh insights and new techniques to use in their own research on open problems.
- Monday, 31 August 2026 - Thursday, 3 September 2026
  Università degli Studi di Padova
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 01 thu 2026

MOX Colloquia
Rainer Helmig, Porous Media Free-Flow Coupling - From REV to Pore Scale and Back, 10-01-2026, 14:30
- MOX Colloquia
- Rainer Helmig
- Professor Emeritus, University of Stuttgart
- Porous Media Free-Flow Coupling - From REV to Pore Scale and Back
- Thursday, 1 October 2026 at 14:30
- Sala Consiglio, Edificio 14, Politecnico di Milano
- Abstract
  
  Flow and transport processes in domains composed of a porous medium and an adjacent free-flow region appear in a wide range of industrial, bio-medical and environmental applications. Industrial applications range from flow in fuel cells to drying processes; possible bio-medical applications include the interplay of distribution processes in blood vessels and in the surrounding tissue. Applications in environmental systems include infiltration of overland flow during rainfall, groundwater contamination due to infiltrating pollutants and evaporation from soil.
  
  One of the key challenges for coupled free flow and porous-medium flow arises from the fact that the overall effective behaviour depends strongly on interface processes that occur on small spatial scales (pore scale), although the overall system of interest is often too large to resolve these processes explicitly in detail. REV-scale models are usually not able to capture all the relevant physical processes for such coupled systems. For the accurate description of interface phenomena, it is therefore necessary to develop model concepts that combine information gained through pore-scale and REV-scale models.
  
  The first part of the lecture includes the following items:
  -an explanation of relevant processes of mass, momentum and energy transfer at the interface between a free-flow and a porous-media system;
  -a presentation of conceptual models for coupled single-phase free flow and two-phase porous-medium flow with a detailed description of the models in the free flow and in the porous medium for the pore and REV scale;
  -comparison studies to show the advantages and disadvantages in relation to classical approaches; the coupling concepts are discussed on the basis of different technical or environmental issues.
  
  In the second part of the lecture I would very much like to discuss the results on the basis of various detailed use cases. These include e.g. aspects of soil evaporation, heat storage in porous media, self-cooling of turbines or the salinization of soils.
  
  This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
  
  Contatti:
  paola.antonietti@polimi.it
- Rainer Helmig
  Rainer Helmig is Professor Emeritus of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart, Germany. He gained his doctoral degree from the University of Hannover in 1993 and a the Habilitation degree from the University of Stuttgart in 1997. In 1995, he was awarded the renowned "Dresdner Grundwasserforschungspreis" for his doctoral thesis. From 1997 to 2000, he held a professorship at the Technical University of Braunschweig. He was co-founder and, from 2009 to 2011, President of "InterPore"; from 2007 to 2015, he was spokesman of the International Research Training Group "NUPUS - Nonlinearities and upscaling in porous media", and from 2018 to 2023 he was spokesman of the Collaborative Research Centre 1313 “Interface-Driven Multi-Field Processes in Porous Media: Flow, Transport and Deformation”. From 2007 to 2018, he was a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is member of Academy of Sciences, Academia Europaea, Heidelberg and acatech. In 2020, he was granted the AGU Fellowship of the American Geophysical Union. In 2022 he got the Honorary Degree of Doctor of Engineering at the Heriot-Watt University. He was awarded the Kimberly-Clark Distinguished Lectureship 2025 and in 2025 he was granted the SIAM Geosciences Career Prize.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 08 thu 2026

oct 09 fri 2026

WorkShop
Algodefi 26: algorithmic trading, decentralized finance and artificial intelligence in capital markets
10/08/2026 - 10/09/2026
- WORKSHOP
- ALGODEFI26
  Algodefi 26: algorithmic trading, decentralized finance and artificial intelligence in capital markets
- organizers
  Emilio Barucci and Michele Azzone
- Dates: October 8–9, 2026 Venue: Department of Mathematics, Politecnico di Milano Submission and registration are open on the conference website. Call for Papers: Accepting full papers or extended abstracts Deadline for Submission: September 1st, 2026 Notification of Acceptance: September 15th, 2026 Deadline for Registration: September 25th, 2026 Keynote Speakers Eduardo Abi Jaber (École Polytechnique) Sebastian Jaimungal (University of Toronto) We will have an industry-Oriented Session in a dedicated afternoon. Scientific Committee Emilio Barucci (Chair), Tomaso Aste, Michele Azzone, Leandro Sánchez Betancourt, Andrea Prampolini Description The landscape of financial markets is changing significantly thanks to new technologies and methodologies that are profoundly modifying their architecture and functioning. Among the innovations, we have the possibility of operating using real-time market information, machine learning techniques, automatic trading strategies, automatic market making, distributed ledger technologies, digital assets, smart contracts, and cryptocurrencies. The objective of the workshop is to offer an opportunity for the academic and industrial communities to meet and discuss research advancements on these topics.
- Thursday, 8 October 2026 - Friday, 9 October 2026
  Department of Mathematics
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 02 mon 2026

nov 06 fri 2026

WorkShop
Model reduction and surrogate modeling 2026
11/02/2026 - 11/06/2026
- WORKSHOP
- MORe2026
  Model reduction and surrogate modeling 2026
- organizers
  Andrea Manzoni (Chair), Nicolò Botteghi, Luca Dede', Nicola Farenga, Nicola Rares Franco, Andrea Manzoni, Simona Perotto, Piermario Vitullo, Paolo Zunino (Organizing Committee)
- This 5-day conference will bring together the international community of computational scientists, engineers, mathematicians, and domain experts from industry, the national laboratories and academia to address the topic of model reduction and surrogate modeling for high-dimensional complex systems.
- Monday, 2 November 2026 - Friday, 6 November 2026
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
feb 08 mon 2027

feb 12 fri 2027

WorkShop
Mathematical challenges in quantum mechanics 2027, school and workshop
02/08/2027 - 02/12/2027
- WORKSHOP
- MCQM27
  Mathematical challenges in quantum mechanics 2027, school and workshop
- organizers
  Michele Correggi (Polimi), Marco Falconi (Polimi), Davide Fermi (Polimi), Angelo Lucia (Polimi), Massimo Moscolari (Polimi), Alessandro Olgiati (Polimi).
- From February 8th to 12th, 2027, the School and Workshop Mathematical Challenges in Quantum Mechanics (MCQM27) will take place at the Department of Mathematics of Politecnico di Milano (Italy). The meeting – at its fifth edition – aims to present the state of the art of challenging open problems in Quantum Mechanics, from the point of view of Mathematical Physics. It will provide a space for scientific exchanges among PhD students and early-career and senior researchers. The program will consist of three introductory mini courses (by Phan Thành Nam, Yoshiko Ogata, Andreas Winter), six invited talks (by Horia Cornean, Marcello Dalmonte, Clotilde Fermanian Kammerer, Paolo Tilli, Katharina Schratz, Giovanni Valente) and contributed talk sessions by selected young participants. Some financial support to young participants will be available. Website: www.mcqm.it This event is part of the activities of the Department of Exellence 2023-27.
- Monday, 8 February 2027 - Friday, 12 February 2027
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 05 mon 2027

jul 09 fri 2027

WorkShop
International conference on spectral and high-order methods
07/05/2027 - 07/09/2027
- WORKSHOP
- ICOSAHOM2027
  International conference on spectral and high-order methods
- organizers
  P.F. Antonietti, N. Parolini, M. Verani (Conference Chairs), C. Canuto, A. Quarteroni (Honorary Chairs), L. Beirao da Veiga, F. Bonizzoni, L. Dede’, I. Fumagalli, P. Gervasio, C. Marcati, L. Mascotto, I. Mazzieri, S. Perotto, G. Sangalli
- Since 1989, the International Conference on Spectral and High-Order Methods (ICOSAHOM) has served as a leading international forum for researchers and practitioners working on the theoretical, computational, and applied aspects of high-order and spectral methods for solving differential equations. The 2027 edition of ICOSAHOM will be proudly hosted by Politecnico di Milano, bringing together experts from around the world to share the latest advances and foster new collaborations in this vibrant field. ICOSAHOM 2027 is a satellite meeting of the 11th International Congress on Industrial and Applied Mathematics (ICIAM), The Hague, The Netherlands, 12-16 July 2027.
- Monday, 5 July 2027 - Friday, 9 July 2027
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

PhD program on

Mathematical Models and Methods in Engineering

PhD Courses